Is there any way to group meshes in a single model to make animating parts of that model easier?
You can work with Vertex Groups which you created in the Vertex Groups panel in the Mesh data tab:



Here you can select and deselect them, rename them, delete them, assign vertices etc. When it comes to animation, you'll propably want to use an armature. Armatures can contain bones, which can be animated (so they contain the keyframes), and by using vertex groups you can tell Blender which vertices to move and how much as soon as you move a bone.